[Abridged] Context. To construct and interpret the spectral energy distribution (SED) of BL Lacertae objects, simultaneous broad-band observations are mandatory. Aims. We present the results of a dedicated multi-wavelength study of the high-frequency peaked BL Lacertae (HBL) object and known TeV emitter 1ES 2344+514 by means of a pre-organised campaign. Methods. The observations were conducted during simultaneous visibility windows of MAGIC and AGILE in late 2008. The measurements were complemented by Metsahovi, RATAN-600, KVA+Tuorla, Swift and VLBA pointings. Additional coverage was provided by the ongoing long-term F-GAMMA and MOJAVE programs, the OVRO 40-m and CrAO telescopes as well as the Fermi satellite. The obtained SEDs are modelled using a one-zone as well as a self-consistent two-zone synchrotron self-Compton model. Results. 1ES 2344+514 was found at very low flux states in both X-rays and very high energy gamma rays. Variability was detected in the low frequency radio and X-ray bands only, where for the latter a small flare was observed. The X-ray flare was possibly caused by shock acceleration characterised by similar cooling and acceleration time scales. MOJAVE VLBA monitoring reveals a static jet whose components are stable over time scales of eleven years, contrary to previous findings. There appears to be no significant correlation between the 15 GHz and R-band monitoring light curves. The observations presented here constitute the first multi-wavelength campaign on 1ES 2344+514 from radio to VHE energies and one of the few simultaneous SEDs during low activity states. The quasi-simultaneous Fermi-LAT data poses some challenges for SED modelling, but in general the SEDs are described well by both applied models. The resulting parameters are typical for TeV emitting HBLs. Consequently it remains unclear whether a so-called quiescent state was found in this campaign.
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